 Angular velocity fixed at birth

Because of the Born rigidity of black holes, it follows directly from a consideration of the Ehrenfest paradox,  that the angular velocity of a black hole can never be changed - it is fixed at birth. To explain this a little more fully, imagine a disk of radius $$R$$ rotating with constant angular velocity $$\omega$$.  Now imagine a reference frame fixed at the centre of the disk, The relative velocity of any point on the disk is given by $$\omega R$$. So the circumference will undergo Lorentz contraction by a factor of

$\sqrt{(1-(\omega R)^2/c^2)}$

whereas the diameter does not.

So we have

$\frac{circumference}{diameter}=\pi\sqrt{(1-(\omega R)^2/c^2)}$

This is paradoxical for a truly rigid body and so in the general case, the body must deform. In the special case of a black hole, because of Born rigidity, deformation is not possible, and hence, the only alternative is that $$\omega$$ is fixed. (Thanks to Wikipedia for this explanation)

When a black hole increases in mass, it must do so in a way that it maintains a constant angular velocity.

## Ultimate size-> 